Cluster Comput (2017) 20:239–252DOI 10.1007/s10586-016-0678-2

Decision support based automatic container sequencing systemusing heuristic rules

Yi Ding1 · Xu-Jun Wei1 · Yang Yang1 · Tian-Yi Gu2

Received: 4 August 2016 / Revised: 21 October 2016 / Accepted: 27 October 2016 / Published online: 10 November 2016© Springer Science+Business Media New York 2016

Abstract Container terminals in seaports constitute inter-faces between the seaborne transport and transport-over-landof goods in global transport chains. The loading and unload-ing of containers are performed using quay cranes (QCs),which is the most important equipment for handling servic-ing vessels at a container terminal. Following tremendousgrowth in global container transshipments, terminals are fac-ing increasing demand. Terminals at Shanghai are equippedwith Tandem Lift which can lift two 40’ containers simulta-neously to improve the efficiency of the QCs. A reasonablecontainer combinations of Tandem Lift and container oper-ation sequence are required to improve the servicing ofvessels, meanwhile the dual cycling container operation ofquay cranes has to be investigated. This paper presents a two-stage mathematical model and two-level heuristic algorithmfor planning the container operation sequence using TandemLift in a feasible computational time. Based on the proposedmethodology, a decision support system, called the TandemLift Container Sequence System (TLCSS). A case study ofShanghai Shengdong International Port Company (SSICT)proves that consideration of the container sequencewith Tan-dem Lift dramatically shortens servicing time of vessels withthe TLCSS.

Keywords Container terminal ·Quay cranes · Tandem Lift ·Container sequence

B Yi Dingyiding@shmtu.edu.cn

1 Logistics Research Center, Shanghai Maritime University,Shanghai, China

2 Department of Computer Science, University of NewHampshire, Durham, NH 03824, USA

1 Introduction

The marine container industry has grown dramatically inthe last three decades, and container transportation hasbecome a predominant mode of inter-continental cargo traf-fic. Container terminals, which are multi-modal inter-facesthat connect sea transportation with land transport, whichplays an important role. To exploit economies of scale, thesize of container ships has significantly increased during thelast few decades. A large container ship typically re-quiresthe lifting of thousands of containers at the terminal duringone call. Since running a container ship involves amajor capi-tal investment and significant daily operating costs, customerservice has become the principal issue at container terminals.More and more container terminals are seeking to improvetheir throughput and reduce the turnaround time of vessels.With containerization increasing, the number of containerterminals has increased substantially and stiff competitionhas developed grown among terminals.

As one of the busiest container ports in the world, theShanghai Port has handledmore than 162million twenty-footequivalent units (TEUs) in the past five years, making it theport with the highest total throughput in theworld since 2010.In 2015, the Port of Shanghai handled an unprecedented 35.2million TEUs, and it is expected to handle evenmore in 2016.

As shown in Table 1, based on current resource allocationstrategy and handling technique, the designed capacity ofShanghai Port is approximately 33 million TEU. Actual con-tainer throughput at Shanghai Port exceeded this designedcapacity by 3.2% in 2015, and this capacity gap will continueto increase with the number of handled containers. Effortsshould bemade to improve container through-put by expand-ing the port or optimizing its operation. Most ports generallyprefer operating optimization because construction to expanda port requires huge investment and takes a long time.

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Table 1 Estimated operational capacity of Shanghai Port

Quantity ofQC NQC

Average efficiencytQC (TEU/h)

AverageutilizationofQC KQC

Berth designed operationcapacity* (TEU) TB

WaiGaoQiao phase I 11 29 60% 1676664

WaiGaoQiao phase II 26 29 60% 3963024

WaiGaoQiao phase IV 16 29 60% 2438784

WaiGaoQiao phase V 16 29 60% 2438784

Yang Shan I 34 32 60% 5718528

Yang Shan III 26 32 60% 4372992

Total 129 180 32974041

*Berth handling capacity TB = NQC × tQC × KQC × 365 × 24*Source: Data on Shanghai International Port Group (SIPG)

Fig. 1 Typical work flow at container terminal

The typical work flow during a loading operation for con-tainer departure that are retrieved from the yard and loadedto a vessel (YV), is as follows. One yard crane (YC) picks upa container from a container block and loads it onto internaltruck internal truck (YT). The YT then transports the con-tainer to a QC (quay crane), which loads the container ontothe vessel. The unloading operation for arrival containers isthe reverse of the foregoing: a container is unloaded froma vessel to the yard (VY). Minimizing vessel handling timeis often a high priority for the quay cranes (QCs), whichtransship the containers between the vessels with terminalquay area.Onemethod for increasing the productivity ofQCsinvolves dual-cycle operations, which comprise both unload-ing and loading operations in one operation cycle. However,the QCs at most container terminals adopt the single cyclemethod, by which a QC performs all loading activities afterall of its unloading activities have been finished. This single-cycle method provides lower QC productivity than the dualcycling model Fig. 1 since the moving of empty is unproduc-tive.

The tandem lift quay crane effectively improves the effi-ciency ofQCoperations. ATandemLift is an extension of thetwin lift, which can lift two 20′ containers end to end. TheTandem Lift quay crane can lift two 40′ containers or twopairs of twin lift containers side by side, as presented in Fig.

Fig. 2 Tandem lift QC

2. Following technological transformation,which takes sometime, TandemLift crane can also lift a single 40′. Meanwhile,the pair of Tandem Lift containers combined by validatingthe position of selected containers in the vessel which mustbe in adjacent slots in the same tier and checking the weightof two containers of each pair of Tandem Lift, slot and tierdenote the relative storage position of vessel as shown in Fig.6. Both of the aforementioned methods improve the opera-tional efficiency of a QC by reducing the number of workingcycles of the QC. Theoretically, the Tandem Lift system candouble the operating efficiency of a QC.

The tandem lift increases the complexity of determinationof the container sequencing in the bay of a vessel. For exam-ple, Shanghai Shengdong International Container Terminal(SSICT) has already equipped its QCs with the Tandem Liftsystem, but only 11% of QC operations were Tandem Lift inDecember 2014, and those Tandem Lift operations improvedefficiency by only approximately 30 percent, from30.44 con-tainers/hour (CPH) to 47.08 containers /hour, as indicated inTable 2.

The above results have the following causes. Firstly,minimizing the service time of a quay crane with a differ-

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Table 2 Tandem lift usage in December 2014 at SSICT

average operationefficiency oftandem lift (CPH)

Average operationefficiency ofQC(CPH)

Containers quantityof handling by tandemlift (containers)

The tandem liftratio (TLR)

Operation time oftandem lift (h)

The ratio of totaloperation time

47.08 28.44 48536 11.08% 1379.62 8.06%

ent lifting approach depends on the reasonable operatingcontainer sequence and manually determining the optimalsequence of operations of a Tandem Lift QC is extremelydifficult/hard/complex. Secondly, convertingQC lift technol-ogy from single lift to Tandem Lift may take a long time, anda poor container sequence solution may increase lift conver-sion frequency. Finally, container pairs for Tandem Liftingare limited by such factors as weight class, height, slot in ves-sel bay. /Hence, the container sequence has a strong impact onthe utilization of Tandem-Lifted. Tandem Lift also requiresthe simultaneous quayside arrival of two trucks, potentiallyincreasing the waiting time of the QC and reducing operatingefficiency. This study proposes a two-stage model for con-tainer sequencing with Tandem Lift. The goal is to minimizethe total time required to perform the container transship-ments at the vessel bay. Only a single bay is considered,because terminal operators avoid frequent repositioning ofthe slow-moving cranes by requiring QCs to process one baycompletely before moving to the next.

2 Literature review

In this section, we introduce some quay crane schedulingproblems under different circumstances in container termi-nals and then briefly describe related methods proposed tosolve these problems.

To improve practical QC scheduling in terms of assumedtime windows during which QCs are assigned to a vessel.Kim and Park [1] developed an effective heuristic searchalgorithm, called greedy randomized adaptive search proce-dure (GRASP). GRASP successfully eliminate the computa-tional difficulty of the previously branch and bound method.Subsequently, the interference among QCs was taken in toconsider. Lee et al. [2] proposed a genetic algorithm (GA) tooptimize the handling sequence for QCs with this premise.

Stahlbock andVoß [3] emphasized that the operation plansin container terminals should be indispensably optimized.They studied various container terminal (CT) operation plan-ning problems, Although the container sequence problem(CSP) has not yet been addressed directly, key related issues,such as crane operations planning, dual cycling, and con-tainer reshuffling, have been investigated in the context ofstowage planning, yard crane scheduling, and QC schedul-ing. Zhu and Lim [4] took the non-crossing constraint into

consider when arranging the QC scheduling plan. Liu etal. [5] also investigated the quay crane scheduling problem.They aimed to minimize the maximum relative tardiness ofvessel departures.

Goodchild andDaganzo [6] firstly incorporated crane dualcycling issues into QC scheduling. Their approach concernsthe operating process of a single QC at a bay of a containervessel. Every container stack in the considered bay is rep-resented by two tasks that are related by precedence, thefirst of which is unloading the stack and the other of which isloading the stack. The processing time of these task are deter-mined by the number of containers to be (un-)loaded. Cranedual cycling is realized by the parallelization of unloadingand loading of different stacks. The purpose is to find asequence for processing stacks that minimizes the make spanof the schedule while maximizing crane dual cycling. Hence,this problem is formulated as a two-machine flow shopscheduling problem, which is solved exactly using the rule ofJohnson (1954). Goodchild and Daganzo [7] proved the eco-nomic benefits of the QC dual cycling, which are increasedcrane productivity, berth utilization, and vessel utilization.Zhang and Kim [8] extended the approach of Goodchild andDaganzo by considering the effect of hatch covers on QCoperations including local search to solve stack-based QCscheduling incorporates dual cycling. Frank and Matthias[9] proved the consideration of internal reshuffles shortensvessel handling time more than crane dual-cycling alone.Zhen [10] studies two tactical level decision problems aris-ing in transshipment hubs: berth template planning that isconcerned with allocating berths and quay cranes to arrivingvessels, and yard template planning that is concerned withassigning yard storage locations to vessels. Chen [11] stud-ied the interactions between crane handling and yard trucktransportation in a maritime container terminal by consider-ing them as simultaneous. They formulated the problem as aconstraint programming model and developed a three-stagealgorithm. Kaveshgar and Huynh [12] developed a mixedinteger programming model for scheduling quay cranes andinternal trucks jointly considering precedence relationshipsbetween containers, blocking, quay crane interference, andquay crane safety margin. This model solved the integratedoptimizationmodelwith a genetic algorithmcombinedwith agreedy algorithm. Delavar and Aryan [13] proposed a hybridheuristic method (HSGA) to find a suitable scheduling forworkflow graph, based on genetic algorithm to obtain the

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response quickly moreover optimizes makespan, load bal-ancing on resources and speedup ratio.

About quay crane scheduling problems, Stahlbock andVoß [3] and Bierwirth and Meisel [14,15] have an overviewon applications and optimization models. Other studies inte-grated with berth allocation management [16–20].

This paper proposes a two-stage Tandem Lift containersequence model, in which containers are paired for Tan-dem Lifting containers in a manner that satisfies the relevantprocessing constraints. Container sequences are optimizedto reduce the make-span service time of QCs in each ves-sel bay. The container sequence problem, as complex stacksequencing problem, becomes more difficult to solve as thenumber of container increases. Therefore, a two-level heuris-tic algorithm is developed for obtaining the optimal containersequence and the pairs of Tandem lift within feasible time.Accordingly, a decision support system (DSS), called theTandemLiftContainer SequenceSystem (TLCSS), that auto-matically generates container sequences with Tandem Lift isdeveloped and implemented at SSICT in Shanghai YangshanPort.

3 Problem description

In the Tandem Lift CSP, an arrival configuration and a depar-ture configuration of containers in each bay are given. Theproblem is to find a sequence of containermoves that convertsthe arrival configuration into the departure configuration inthe shortest possible service time of the bay, each smallsquare denote one container and these containers are posi-tioned by units of bay, slot, tier, as presented in Fig. 3.Theservice time of the bay is defined as the total time to performthe required container moves and the empty crane moves,taking into account time required to shift switch betweenSingle Lift and Tandem Lift. A solution to the problem mustrespect the stacking-dependent accessibility of the contain-ers. The twomost important types of container move that canbe performed by QC are denoted as VY and YV.

Each QC action is called a move. One move of a singlecycling can be a VY or an YV operation which must makean“empty move” before the next move. However, in dualcycling, VY and YV moves are successively made withoutan empty move in between. The two types of dual cycle areYV followed by VY or VY followed by YV, which havedifferent transfer times. VY to YV requires more waitingby the internal trucks than YV to VY, because dual cyclingfrom VY to YV requires two (pair of) trucks, whereas YVto VY requires only one (pair). The situation is the samewhen Tandem Lifts are used, except that double the numberof containers are loaded and unloaded per move.

To evaluate a containermove sequence based on the result-ing service time of the bay, the time to move the containers,

Fig. 3 Configuration diagram of vessels

Table 3 Time to empty crane lift movement and lift transform (s)

Single lift Tandem lift

YV VY YV VY

Single lift YV 60 0 360 300

VY 20 60 320 360

Tandem lift YV 360 300 60 0

VY 320 360 20 60

Processing time: YV:110, VY:90

the number of empty lift moves and the time to transform lifttechnology must input to solve the Tandem Lift CSP. To sim-plify the formulation of the CSP, the slot-specific containermove perform time is neglected. Rather, the time to process-ing a container move is assumed to depend merely on thetype of the move. A rough estimate of processing time canbe derived by assuming that aQCmakes around 30moves perhour, which value is typical nowadays. So Each VY and eachYV operation are assumed to take 90 and 110 s, respectively(including lifting, moving, and loading). YV involves wait-ing for a truck with a specific container, as determined by theloading sequence, which increases potential waiting time forthe trucks. A move of an empty crane lift is assumed to take60s. The time required for an empty crane lift move betweentwo consecutive container moves depends on whether dualcycling is being performed. The time to transform betweena Tandem Lift and a Single Lift is long, averaging approx-imately 300s. Table 3 presents estimated processing timesfor container moves and empty crane lift moves. Section 5presents more accurate times that are estimated from histor-ical operating data from the DSS.

4 Formulations

4.1 Fundamental assumptions

A1. We have rewrite the A1(assumption 1) to add moredetails. The number of QC cycles is used as a unit for

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the time required by a QC to complete all loading orunloading operations in a vessel-bay. Fewer cycles cor-respond to a shorter operation time, or faster service: ifone container is unloaded and one is loaded by a tandemspreader in one dual-cycle, then the number of cycles isone with both loading or unloading in one cycle; other-wise, if these operations are conducted separately, thenthe number of cycles is two, one cycle for loading andthe other one for unloading, as shown in Fig. 1.

A2. The operations of the QCs are the bottleneck duringvessel loading and unloading process, so the through-put rate of QCs determines the throughput rate of theintegrated handling system that is composed of QCs,transporters, and yard cranes. The waiting by QCs for(internal trucks) is ignored, so (internal trucks) arealways immediately available to a QC.

A3. The times to perform an operation vary negligiblyamong containers.

A4. The sizes of all containers are approximately equal thetotal size of two 20ft containers equals that of one 40ftcontainer.

A5. The type of operation conducted on all containers areapproximately the same in the tandem lift containerscombination model, which means all containers areeither loaded (YV) or unloaded (VY).

A6. The operation sequence of each container is pre-decidedbefore tandem lift containers combination model. Theoperate order could be decided by experiences suchas unloading containers from landside to quayside andloading from opposite direction.

Indices

I Set of containersK Set of maximum tandem lift container pairs

Parameters

di j Distance between container i and container jD Positive integer, equals 1. The maximum distance

between two containers with Tandem-Liftedwi j The difference of the weights of container i and con-

tainer jW The maximum difference of the weights of two con-

tainers of Tandem Lift pair.n The minimum sequential number of Tandem Lift con-

tainer pairs combinedQ Number of containersqi The loading or unloading sequence number (LUN) of

container its The handling time of a single lifttt The handling time of a Tandem Lift

Decision values

xi jk Binary, equals to 1 if containeriand container jarecombined by tandem lift, 0 otherwise

yi jk Binary, equals to 1 if containeri and container jarecombined with other containers, but they arein a same sequential tandem lift operation sequence,0 otherwise

zi Binary, equals to 1 if containeri is combined by tandemlift, 0 otherwise

Objective function

min

⎧⎨

⎩ts Q +

(tt2

− ts

) Q∑

i=0

zi

⎫⎬

⎭(1)

The objective function is tominimize the sum of the handlingtimes of both single-lifted and Tandem-Lifted containers.

Subject to

xi j = x ji ,∀i, j ∈ I (2)

Q∑

i=0

∣∣qi − q j

∣∣xi j ≤ 1,∀ j ∈ I (3)

Q∑

i=0

di j xi j ≤ D,∀ j ∈ I (4)

Q∑

i=0

wi j xi j ≤ D,∀ j ∈ I (5)

Q∑

j=0

xi j ≤ zi ,∀i ∈ I (6)

max(i, j)∑

k=min(i, j)

zk ≥ (∣∣qi − q j

∣∣ + 1

)yi j ,∀i, j ∈ I (7)

Q∑

j=0

yi j ≤ 2n ∗ zi ,∀i ∈ I (8)

xi j = 0, 1,∀i, j ∈ I (9)

yi j = 0, 1,∀i, j ∈ I (10)

zi = 0, 1,∀i ∈ I (11)

Constraints (2) and (3) ensure that a container is combinedwith no more than one other container that follows or pre-cedes it in the loading or unloading sequence. Constraint (4)

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Fig. 4 Example of distance between containers

ensures that the distance between two combined containersis less than an upper bound, D. Usually, D equals one. Forexample, in Fig. 4, the blue container may be combined withC as Tandem Lift pair with the distance restriction, but thered one may not be. Constraint (5) ensures that the differ-ence between the weights of paired containers is less thanan upper bound. Constraint (6) ensure that if a container iscombined with another, then it is defined as a combined con-tainer. Constraint (7) ensures continuous tandem lift handlingof containers whose handling on-going between that of con-tainer i and that of container j . Constraint (8) ensures thatonce a tandem lift is used, the QC must perform at least ntandem lift moves without interruption. Constraints (9)–(11)set the binary variables to zero or one.

4.2 Fundamental assumptions

Sets

I Set of loading containers including tandem lift containerpairs which obtain from model I as one container task.

J Set of unloading containers including tandem lift con-tainer pairs which obtain from model I as one containertask.

K Set of task sequence ordersH Set of loading container pairs (i , j), in which container

i and j are located in the same bay slot and the prece-dence order number of container i is greater than that ofcontainer j

G Set of unloading container pairs (i , j), in whichcontaineri and j are located in the same bay slot and theprecedence order number of container i is greater thanthat of container j

L Set of loading and unloading container pairs (i , j), inwhich loading container i and unloading container j arelocated in the same bay slot

Parameters

di j The difference distance of the slots of loading containeri and unloading container j

hi The precedence order number of loading container i

g j The precedence order number of unloading container jti j The handling time of a dual cycling loading container i

and unloading container j .tl A handling time of a loading container.tu A handling time of an unloading container.ts A time in-between query empty lift movement time of

single cycletd A time in-between query empty lift movement time of

dual cyclingN Number of loading containersM Number of unloading containersP Maximum moves of query craneD The maximum difference distance of the slots of loading

container and unloading container could be combinedtogether as dual cycling.

Decision values

xi jk Binary, equals to1 if loading container i and unload-ing container j are combined in one cycle, which isthe k cycle in order sequence, 0 otherwiseThe bit 0 of i and j is the virtual loading and unload-ing container, that a container combined to whichmeans it will be operated without dual cycling.

Objective function

min tl

P∑

k=0

M∑

j=1

x0 jk +P∑

k=0

M∑

i=1

xi0k +N∑

i=1

M∑

j=1

ti j

P∑

k=0

xi jk

+ ts

⎛

⎝P∑

k=0

M∑

j=1

x0 jk +P∑

k=0

M∑

i=1

xi0k

⎞

⎠ + td

P∑

k=0

N∑

j=1

M∑

i=1

xi jk

(12)

The objective function is tominimize the sum of the handlingtimes of all containers and the times between all query cranelift movements.

Subject to

P∑

k=0

N∑

i=0

xi jk = 1,∀ j ∈ J, j �= 0 (13)

P∑

k=0

M∑

j=0

xi jk = 1,∀i ∈ I, i �= 0 (14)

P∑

k=0

x00k = 0,∀k ∈ K (15)

N∑

i=0

M∑

j=0

xi jk ≥N∑

i=0

M∑

j=0

xi jk+1,∀k ∈ K (16)

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P∑

k=0

M∑

j=1

di j xi jk ≤ D,∀i ∈ I, i �= 0 (17)

P∑

k=0

N∑

i=1

di j xi jk ≤ D,∀ j ∈ J, j �= 0 (18)

P∑

k=0

M∑

j=0

kxi jk ≤P∑

k=0

M∑

j=0

kxq jk,

∀i, q ∈ I, i �= 0, q �= 0, (i, q) ∈ H (19)

P∑

k=0

N∑

i=0

kxi jk ≤P∑

k=0

N∑

i=0

kxipk,

∀ j, p ∈ J, j �= 0, p �= 0, ( j, p) ∈ L (20)

P∑

k=0

N∑

i=0

kxipk ≤P∑

k=0

M∑

j=0

kxq jk,

∀q ∈ I, q �= 0, p ∈ J, j �= 0, p �= 0, (p, q) ∈ L (21)

N∑

i=0

M∑

j=0

xi jk ≤ 1,∀k ∈ K (22)

xi jk = 0, 1,∀i ∈ I,∀ j ∈ J,∀k ∈ K (23)

Constraints (13) and (14) ensure that each loaded andunloaded container is handled exactly once. Constraint (15)ensures that each virtual loaded or unloaded container isnot combined with another virtual container. Constraint (16)ensures that no interrupt should exist in the middle of thetasks sequence. Constraints (17) and (18) ensure that the dif-ference between two combined containers’ slot number isless than an upper bound. Constraints (19) and (20) ensurethat the handling of all containers is consistent with theirphysical positions. Constraint (21) ensures that the load-ing and unloading of containers in a single bay slot followsFirst Unloaded, Then Loaded (FUTL) rule. Constraint (22)ensures that each cycle of each query crane should performeither a single container task or two du-al-cycling containertasks. Constraint (23) sets binary variables to one or zero.

CHS model provides the handling sequence of all con-tainers. An iterative search is required because the output ofthe Model I might cut some better solution of model II. Thefollowing section proposes a two-level metaheuristic methodfor finding the optimal solution, which is designed accord-ing to the features of the Tandem Lift CSP, and this methodforms the basis of an algorithm for the DSS system.

5 Heuristic approach to tandem lift CSP

The two-stage model is a master-slave model, in which para-meters are transferred from master to the slave to obtain

Ini�al solu�on for container handling sequence

2leveL1leveL

Select the best admissible solu�on

Fitness evalua�on by LP relaxa�on

Building the candidate combina�on solu�on

Create neighborhood solu�ons

Stopping criterion for Model 1

Sa�sfied

Get Ini�al container sequence from Candidate List

Get the Tabu-search solu�ons

Select the best admissible solu�on

Stopping criterion for Model 2

sa�sfied

END

NO

YES

YES

Con�nue itera�on

containers Tandem Li� or not

Fig. 5 Flow chart of the two-level heuristic

the optimal objective function value by slave stage. Find-ing the optimal solution is difficult owing to the complexityof the two-stage programming model. Therefore, a two-levelheuristic approach for finding sub-optimal solutions withina short computational time is proposed, and then a DSS forthe Tandem Lift CSP is developed based on this two-levelheuristic, as described in Sect. 6.

5.1 Framework of two-level heuristic

The proposed heuristic for solving the Tandem Lift CSP ishierarchical, as shownby the heuristic flowchart inFig. 5. Theheuristic comprises two levels. Level 1 yields pairs ofTandemLifting containers in a vessel bay. In this level, a neigh-borhood search technique is utilized to improve solutionsthroughout the search. Linear programming relaxation is per-formed to solve the Container handling sequence (Model2) problem to evaluate efficiently the fitness of the solu-tions. At the end of level 1, a good Tandem Lift ContainersCombination solution is output and passed into level 2. Theobtained pairs of Tandem Lifting containers are input and adetailed container handling sequence is deter-mined in level2. The sub-problem of Level 2 is a scheduling problem withprecedence constraints whose processing time is affectedby scheduling sequence [21]. A Tabu search-based heuris-tic method is proposed herein to find a good solution to theTandem Lift CSP and the total cost of moving containers ina vessel bay is obtained.

5.2 Level-1 of heuristic

This Level beginswith an initial container handling sequencethat is obtained beforemaking a pairs of TandemLifting con-tainers solution. In the absence of dual cycling, the operatorof a container terminal chooses a simple sequence in which

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Fig. 6 Initial container handling sequence

to unload all import containers from the landside to the quay-side slot by slot and then to load all export containers in theopposite direction, as presented in Fig. 6. Each containermaybe combined with two adjacent containers without consid-eration of the weight of each container, so the number ofcombinations of containers for Tandem Lifting is high.

Basing on the simple initial container handling sequence,a set of feasible initial solutions to the Tandem Lift containercombination problem is randomly generated including bothan arrival configuration and a departure configuration for avessel bay. The following straightforward encoding represen-tation of the Tandem Lift Container combination problem isutilized herein. Let (t1, t2, . . . , ti ) represent chosen contain-ers to be combined with container i where component ti isdenotes the container that is combined with container i ∈ Q;ti =1 or 2 specifies that container i is combined with thecontainer to its left or right; ti = 0 indicates no combination.

For example, T = (2,1,0,0,2,1,2,1,0) is a combinationof nine containers, as presented in Fig. 6. In this solution,container 1 is combined with container 2 in a Tandem Lifttask. The other two TandemLift container pairs are (5, 6) and(7, 8). Containers 3, 4 and 9with values of 0 are not combinedwith any other container, and so cannot be Tandem Lifted.

Two neighborhood structures are utilized in the neigh-borhood search process, as displayed in Fig. 7; they are thepair-wise interchange and flipping patterns. In Pattern 1, twocomponents of the solution are randomly selected and inter-changed with each other. Pattern 2 only operations on onecomponent. The value of this component is randomly gen-erated and the component ti randomly flipped to {0, 1, 2}.It is essential to adjust the relevant components to make theneighborhood reasonable in both Pattern 1 and Pattern 2. Aspresented by Fig. 7. Two patterns of neighborhood search areimplemented with equal probability.

2 1 0 0 2 1 2 1 0 2 1 0 0 2 1 2 1 0

2 2 0 0 2 1 1 1 0

0 2 1 0 2 1 1 0 0

2 1 0 2 2 1 2 1 0

2 1 0 2 1 0 2 1 0

Selected components Selected components

Pair-wise interchange Flipping

Relevant adjust Relevant adjust

original solu�on

neighborhood solu�on

Fig. 7 Two patterns of neighborhood search

In the next step, sets I and J which respectively are load-ing and unloading containers including pairs of Tandem LiftContainers as operating tasks, obtained from level 1 of theheuristic. The overall optimization of Two-stage model isunfeasibly difficult, if dual cycling in Model 2 is taken intoaccount in Model 1. To evaluate the combination of con-tainers solution for Tandem Lifting, the linear programmingrelaxation is used by replacing the binary constraint in model2 with a weaker constraint which belongs to the interval [0,1]. The relaxed linear program of the remaining ContainerHanding Sequence problem (model 2) is as follows.

min (12) + F(xi j

)(24)

St. (13) − (23)

xi jo ∈ [0, 1]

xi j denotes the combination of containers forTandemLift-ing that is obtained using Model 1. If xi j violates constraints(2)–(11) in model 1, then a penalty function is added to thefitness function. The objective function (12) and the penaltyfunction F(xi j )yield thefitness function in the level-1 heuris-tic. The linear programming relaxation of model 2 indicatesa possible lower bound on the processing time of TandemLift CSP problem based on a given combination solution ofcontainers for Tandem Lifting.

The neighborhood search that is performed in solving theTandem Lift container combination problem in Level 1, isterminated when the best solution does not change with aspecified number of consecutive iterations. then the solutionof Tandem Lifting or not for each container are transfer toLevel-2 heuristic as input data.

5.3 Level-2 of heuristic

The Tandem Lift CSP is a deterministic single machinescheduling problem [14] in which the total processing time

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Cmin is minimized considering container stacking prece-dence pi j , which is determined by the stacking configuration,as presented in Fig. (3). The total processing time ri j is influ-enced by the scheduling sequence and consists of three parts,the processing time for container moves t j , the empty cranemovement t ime · ti j , and the time to transform the TandemLift li j .

ri j = t j + ti j + li j (25)

Each i , j pair indicates a movement of a container or a pair ofTandem Lift containers (load or unload). The time to processcontainer move t j is determined by the type of operation,and ti j + li j depends on the container handling sequence; theobjective is to minimize the total ti j + li j for each vessel bay.

Above the hatch, no export containers canbe loadedbeforeall the import containers are unloaded, so dual cycling isnot considered. Without dual cycling, the simple containersequence is obtained by the level-1 heuristic.

The Tandem Lift CSP below the hatch can be representedin very elegantly as a directed graph. Consider a directedgraph G with a set of nodes N ′ and two sets of arcs A andB; the nodes N ′ correspond to all operations (i slot i ) thatmust be performed on the M ∪ N loaded and unloaded con-tainers, where i , and slot i is the slot number. The solid arcsA represent the routes of relative priorities for all contain-ers. If A includes arc (i , slot i ) →( j , slot j ), then containeri must be processed in slot i before container j . If two con-tainers are combined for Tandem Lifting, then they must beprocessed simultaneously after all preceding containers havebeen completed. Arc B indicates the container sequence ofcontainers, which includes two types of container move (YVor VY). So the Arcs B could be represented both dual cyclingoperations and the Tandem Lift dual cycling operations.

This directed graph is denoted as G = (N′, A, B), anddisplayed in Fig. 8). A feasible sequence involves a selectionof arcs B from which a directed graph is constructed suchthat relative priorities represented as arcs A are not broken.The minimization of the make-span of a feasible sequenceis reduced to finding a selection of arcs B that is the shortestpath in G (B) from the source U to the sink V. This shortestpath comprises a set of arcs B of which the first begins attime 0 and the last finishes after the period of the make-span.

In level-2 of heuristic, Tabu-Search, which is used tofind a better feasible sequence of Tandem Lift CSP. TheTabu-Search begins with an initial solution, which may begenerated arbitrarily, and tries to improve upon the currentsolution. Tabu-search moves from one sequence of the Tan-dem Lift CSP to another for a potential candidate such thatthe next sequence may be worse than the one before. In allstages of the process, a Tabu-list of mutations, which theprocedure is not allowed to make, is kept.

Fig. 8 Directed graph represents tandem lift CSP

The initial solution could be generated constructed byextending a partial solution to the tandem lift CSP.Moves thatcould feasibly extend the current partial solution are identi-fied and stored in a so-called candidate list (CL). Initially,when the partial solution is empty, CL includes un-loadingmoves for import containers that are located on top of slots inthe arrival configuration and moves for loading export con-tainers into empty slots.More precisely, amove for unloadinga container is added to CL as soon as all containers on top ofthis container in the arrival configuration have been removed.A move for loading a container is added to CL as soon as allcontainers that are stacked below this container in the depar-ture configuration have been loaded. Since slots cannot beginto load before its unloading is completed, frequent switch-ing among slots to unload slows service. Therefore, if theQC has begun to unload from a slot, then the unloading ofcontainers from other slots will be postponed by eliminat-ing the corresponding moves from CL, but the moves forloading containers will be added to the CL to increase theprobability of dual cy-cling. As soon as the slot has beencompletely unloaded, all unloading moves are again addedto CL, enabling the selection of a new slot form which a con-tainer can be unloaded. Based on the CL, the initial solutionis gradually constructed step by step by adding one containerat a time, taken at random from CL.

High-quality solutions to a Tandem Lift CSP include ahigh proportion of crane dual cycles for loading and un-loading containers, including Tandem Lift dual cycles, andthey minimize the make-span without violating the feasi-bility of the relative priorities that were defined by arcs A.Therefore, heuristic solutions may be improved by shifting

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one container move to another sequence position, which islimited by the containers stacked above and below the con-sidered container. The improvement procedure examines theshift-neighborhood of a given solution by considering themoves in the sequence solution one by one. The overall pro-cedure of the Tabu-Search algorithm for solving the TandemLift CSP is as follows.

Step 1. Input directed graph G= (N′, A, B) for a vessel baywhere B is empty.Set k = 1.Select an initial sequence B1 at random from a listof candidates, one item at a time.Set B = B1.

Step 2. Select a candidate sequence Bc from the shift-neighborhood of Bk without violating constraintsof arcs A.If the shift Bk → Bc is prohibited by a mutationin the Tabu-list,Then set Bk+1 = Bk and go to Step 3.If the shift Bk →Bc is not prohibited by anymuta-tion in the Tabu-list,Then set Bk+1 = Bc and Add reverse mutation tothe top of the Tabu-list. Push all other entries in theTabu-list one position down andDelete the entry at the bottom of the Tabu-list.If G (Bc) < G (B),set B = Bc;Go to Step 3.

Step 3. Increase k by 1.If k = N, then STOP and return B as Tandem LiftCSP solution.Otherwise go to Step 2.

6 Decision support system

To support practical Tandem Lift container sequencing for aQC, a DSS, called a tandem lift container sequence system(TLCSS) whose embedded kernel is above two-level heuris-tic algorithm, is implemented to yield the optimal solution;it can be rapidly adjusted to suit operational requirements.

Shanghai container terminals have a modular terminaloperating information system (TOS) that provides a fullrange of functions in support of the planning and controloperations. The TOS is directly connected to the operationaldatabase (ODB) and provides information required for themanagement of the operations department.

Fig. 9 shows the integrated framework of the TLCSS andthe data flows among the module components. All the inputdata for the optimizer are taken from twodata-bases-theODBand the historical data warehouse. The ODB stores generalterminal configurations (the number of available QCs, theirattributes, the length of the quay and others), operations datainformation concerning operating containers, arrival config-uration, departure configuration, vessel structure, and so on,which are filtered and organized in the TOS modules to beinput to the optimizer, and the parameters of the algorithm(weight and height settings for Tandem Lift, and so on).Historical operational data are extracted from the ODB andtransferred to the data ware-house periodically (nightly) byETL tool. These historical data are analyzed by using a sta-tistical toolkit to generate the QC productivity profiles thatare described in Table 2, which are fed to the DSS to gen-erate the QC make-span of the vessel bay and the TandemLift container sequencing solution. Before the optimizer isexecuted, all input data are preprocessed by a preprocessor,which validates and checks these input data. The preproces-

Fig. 9 Framework of the TLCSS

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Fig. 10 Shanghai Shengdong International Container Terminal(SSICT)

sor standardizes the data that are required for the developedalgorithm and ensures the successful execution of the opti-mizer.

The TLCSS uses some software architecture with the TOSthat is based on the Microsoft.Net framework. Accordingly,without complicated data adapters, the TOS vessel operationmodules can easily be obtained the solutions that are gen-erated by the TLCSS and display them on a UI with whichthe operator is familiar. Hence, the operator can convenientlymodify and evaluate their Tandem Lift container sequencesfor loading and unloading operations.

7 Case study

TheDSSdeveloped above has been implemented at ShanghaiShengdong International Container Terminal (SSICT) whichis the largest container terminal in the Shanghai port, throughwhich pass import, export and transshipment (domestic andinternational) containers, as displayed in Fig. 10. SSICTis part of the Yangshan Deep-water Port (YDP), which islocated on theYang-Shan Island to the southeast of Shanghai.It has 34 quay cranes (QCs), has a 3000m-long straight-linedquay, and a container yard with an area of 15 hectares. Everymonth, these resources serve more than 550 deep-sea andfeeder vessels, yielding an average throughput of 0.45 mil-lion TEUs. This case study demonstrates the effect of theDSS on container terminal operations at SSICT.

7.1 Tandem Lift CSP for a vessel bay

In Fig. 11, 127 containers are under the hatch cover of onevessel bay (THALASSA AXIA), containing 68% importcontainers and 32% export containers. A heuristic solution tothe Tandem Lift CSP is obtained from the two-level heuris-tic in the TLCSS, yielding a make-span of 164.2 min (9854s). The number of node in the solution simply indicates thesequence of moves for a particular bay, that containers ofeach Tandem Lifting pair have some number of sequence.The solution to the Tandem Lift CSP could be evaluated in

Fig. 11 Tandem lift container sequencing for a vessel bay

terms of various indicators, including the dual cycling ratio(DCR), the Tandem Lift ratio (TLR), the Tandem Lift dualcycling ratio (TLDCR), themake-span time (MT) and theQCefficiency (QCE) which are 51, 88, and 50% and 164.2 min,47 containers/hour, respectively, in this instance. The DCRinclude TLDCR and normal dual cycling operation withoutTandemLift, the higher TLR, TLDCR,DCRcause the higherQCE and lower MT. The two-level heuristic algorithm hasa strong tendency to increase the dual cycling ratio and theTandem Lift ratio. The computational time of the two-levelheuristic algorithm on an application server with a Xeon E52600 CPU and 32 GB DDR of memory is around 23s in thiscase.

7.2 Performance of TLCSS in solving tandem lift CSP

To prove the effectiveness of the two-level heuristic imple-mented in the TLCSS system, the operational data concern-ing 136 vessel bays in ten vessels are collected from SSICT.The sizes of the vessel bays range from 10 to 24 slots. Theseinstances are distinguished by their proportions of importand export containers in the arrival and departure configura-tions, which drastically affect the up-per bound on the dual

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cycling ratio. Hence, an indicator of the number of importcontainers to the number of export containers (IER) is pro-posed, which increases the probability of dual cycling whenreaches a proportion of 1:1. The quality of solutions that areobtained using the heuristic algorithm in the TLCSS systemis evaluated in terms of the relative error (RE) of the ratio ofthe objective function value Z to the lower bound ZCPLEX,where RE= (Z -ZCPLEX)/ ZCPLEX×100. ARE representsthe average relative error (RE) of all bays in one vessel.

The use of multithread technology for parallel computingenables solutions to the Tandem Lift CSP for all bays in eachvessel to be obtained almost simultaneously. The results ofthis application are summarized in Table 4.

One-hundred and thirty-six Tandem Lift CSPs thatinvolved ten vessels in Table 4 were solved using bothCPLEX and the developed two-level heuristic. Fig. 12.shows the computational times in all instances. The com-putational time of the CPLEX increased rapidly with thetotal number of handled containers. However, the two-levelheuristic approach yielded the sub-optimal solutions with-in reasonable time. The range of ARE was from 0.89 to1.97% for different size of vessels. The CPU time was lessthan 30s. These results reveal that two-level heuristic in theTLCSS generates solutions of high quality and is effectivefor instances of various vessel’s sizes. The developed two-level heuristic approach yields sub-optimal solutions withina relatively short computational time, and the heuristic algo-rithmwas not overly sensitive to the size of the problem, so itcan be applied to solve the Tandem Lift CSP for even largervessels.

To provide insight into the structure of the solutions thatwere obtained by the two-level heuristic, Table 4 presentsseveral performance measures for instances of various sizesand workloads. The reported double cycling ratio TLDCR isthe number of TandemLift loading and unloadingmoves thatare performed in dual cycling divided by the total number ofloading and unloading moves. The average IER, TLR, DCRand TLDCR were 0.67, 28.81, 49.25, and 11.14%, respec-tively.

The benefit of Tandem Lift technology in QCs operationis obvious, and the balanced numbers of import and exportcontainers enabled high-frequency dual cycling in the han-dling of containers. The QCE reaches 58.39 containers/h; theaverage QCE equals to 44.71 containers/hour, and has thepotential to be further improved. This result demonstratesthat the proposed approach can greatly increases the QCE interminals. Also, as the total number of containers increases(for unloading and loading), the operational efficiency can beimprovedby reducing the total number of cycles ofQCopera-tions with dual cycling. However, thus improvement dependson a balance between the numbers of import and export con-tainers. Unbalanced IER or vessel stowage con-figurationthat ignores the possibility of combining containers for Tan- Ta

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Fig. 12 The computational time for different number of handing con-tainers

demLifting reduce the utilization ratio of theTandemLift anddual cycling, lowering the efficiency of QC operations. Werecommend that shipping companies and terminals increasethe probability of using Tandem Lift and dual cycling byimplementing with the vessel stowage configuration and tan-dem lift container sequence cooperatively that enable evenfaster vessel loading and unloading at container terminals.

8 Conclusions

Container terminals are equipped with tandem lift QCs forthe efficient servicing container vessels. A two-stage math-ematical optimization model was formulated for solving thetandem lift problem, which reduces the make-span of ves-sel bays by combining containers for Tandem Lifting andthe dual cycling operating containers. Since the model istoo complex to be solved optimally analytically, a two-levelheuristic algorithm is proposed. A case study of a large set ofreal vessel’s instances is presented to demonstrate the effec-tiveness of the developed approach, based on a DSS system,called TLCSS. The results reveal that, on average, approxi-mately 49.25% of loading and unloading operations can beperformed in dual cycles (DCR) and that 28.81% of con-tainers in vessel bays can be combined in Tandem Lift pairs(TLR), with 11.14% Tandem Lift dual cycles (TLDCR). Thepeak efficiency of QC is 58.39 containers/hour, and the meanQCE is 44.71 containers/hour, with room for improvement.

Future works should consider QC operation assignmentunder uncertainty [11] with the optimization of the inte-gration of the QCs and yard machines to improve thecoordination between vessel bay container sequencing andyard operations.

Acknowledgements We would like to express our gratitude to all theemployees at SSICT for their full support in this project. In particular,we thank Mrs. Liang Hong Shen, senior manager of the informationdepartment, for her valuable suggestions onmodeling and system imple-

mentation. This project is partially supported by the National NaturalScience Foundation of China. [71301101] [11302125].

Compliance with ethical standards

Conflicts of interest The authors confirm that this article content hasno conflicts of interest.

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Yi Ding is a Lecturer at theLogistics Research Center ofShanghai Maritime Universitywhere he obtained his doctoraldegree in Logistics Engineeringhe has ten years of experiencein developing container termi-nal operating systems and somedecision support systems for portoperations His research focuseson optimization of container ter-minal operations and informa-tion systemsHe has authored onebook and some journal papers inthese fields.

Xu-Jun Wei is currently a post-graduate of Logistics ResearchCenter at Shanghai MaritimeUniversity in China. He receivedthe Bachelor Degree in IndustrialEngineering fromShanghaiMar-itime University. Weis currentresearch interests include opera-tion research, cost management(port direction) and intelligentalgorithm.

Yang Yang is currently a post-graduate of Logistics ResearchCenter at Shanghai MaritimeUniversity inChina. She receivedthe Bachelor Degree in Logis-tics Engineering from ChangshaUniversity of Science & Tech-nology. Yangs current researchinterests include port operation.

Tian-Yi Gu is currently a Ph.D.Student of Department of Com-puter Science at University ofNew Hampshire in USA. Hereceived the Master Degree inLogistics Research Center fromShanghai Maritime University.Gus current research interestsinclude operation research, engi-neering optimization and intelli-gent algorithm.

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